noun, plural topologies for 3. Mathematics.
the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching.
Also called set topology">point set topology. the study of limits in sets considered as collections of points.
a collection of open sets making a given set a topological space.

1650–60; topo- + -logy

topologic [top-uh-loj-ik] , topological, adjective
topologically, adverb
topologist, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
topology (təˈpɒlədʒɪ)
1.  the branch of mathematics concerned with generalization of the concepts of continuity, limit, etc
2.  Former name: analysis situs a branch of geometry describing the properties of a figure that are unaffected by continuous distortion, such as stretching or knotting
3.  maths a family of subsets of a given set S, such that S is a topological space
4.  the arrangement and interlinking of computers in a computer network
5.  the study of the topography of a given place, esp as far as it reflects its history
6.  the anatomy of any specific bodily area, structure, or part

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Science Dictionary
topology   (tə-pŏl'ə-jē)  Pronunciation Key 
The mathematical study of the geometric properties that are not normally affected by changes in the size or shape of geometric figures. In topology, a donut and a coffee cup with a handle are equivalent shapes, because each has a single hole.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Computing Dictionary

topology definition

1. The branch of mathematics dealing with continuous transformations.
2. Which hosts are directly connected to which other hosts in a network. Network layer processes need to consider the current network topology to be able to route packets to their final destination reliably and efficiently.
The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
It's easy to remember if you note its similarity to topology or topography.
Furthermore, these devices may also be moving, so that the network topology is
  in constant flux.
The secret to this trick comes from a branch of mathematics called topology.
Pragmatism also prevailed in the network's topology.
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